Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Quantum computation and quantum information
Quantum computation and quantum information
Parallel Quantum Computation and Quantum Codes
SIAM Journal on Computing
The Hidden Subgroup Problem and Eigenvalue Estimation on a Quantum Computer
QCQC '98 Selected papers from the First NASA International Conference on Quantum Computing and Quantum Communications
Fast parallel circuits for the quantum Fourier transform
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Arithmetic on a distributed-memory quantum multicomputer
ACM Journal on Emerging Technologies in Computing Systems (JETC)
An efficient conversion of quantum circuits to a linear nearest neighbor architecture
Quantum Information & Computation
Quantum addition circuits and unbounded fan-out
Quantum Information & Computation
Shor's discrete logarithm quantum algorithm for elliptic curves
Quantum Information & Computation
A quantum circuit for shor's factoring algorithm using 2n + 2 qubits
Quantum Information & Computation
A linear-size quantum circuit for addition with no ancillary qubits
Quantum Information & Computation
Entanglement and its role in Shor's algorithm
Quantum Information & Computation
The quantum fourier transform on a linear nearest neighbor architecture
Quantum Information & Computation
Implementation of Shor's algorithm on a linear nearest neighbour qubit array
Quantum Information & Computation
A fast quantum circuit for addition with few qubits
Quantum Information & Computation
Problems of Information Transmission
ETRICS'06 Proceedings of the 2006 international conference on Emerging Trends in Information and Communication Security
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We try to minimize the number of qubits needed to factor an integer of n bits using Shor's algorithm on a quantum computer. We introduce a circuit which uses 2n + 3 qubits and 0(n3lg(n)) elementary quantum gates in a depth of 0(n3) to implement the factorization algorithm. The circuit is computable in polynomial time on a classical computer and is completely general as it does not rely on any property of the number to be factored.